EduSahara™ Worksheet

Question 1

1.

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 20 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?

(i)

26 min 19 sec
(ii)

27 min 20 sec
(iii)

29 min 22 sec
(iv)

25 min 17 sec
(v)

28 min 21 sec

Question 2

2.

A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 60° and 45° and the distance between them is 245 m , find the height of the cliff.

(i)

155.33 m
(ii)

130.33 m
(iii)

161.33 m
(iv)

173.33 m
(v)

151.33 m

Question 3

3.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
60°
.
If the distance between the point and the top of the
tower
is
90 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

45

m
(ii)

46

m
(iii)

48

m
(iv)

44

m
(v)

43

m

Question 4

4.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?

(i)

∠e
(ii)

∠g
(iii)

∠f
(iv)

∠d

Question 5

5.

From the top of a 14 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Find the height of the cable tower.

(i)

61.00 m
(ii)

51.00 m
(iii)

53.00 m
(iv)

59.00 m
(v)

56.00 m

Question 6

6.

An observer 1.6 m tall, is 80 m away from a tower . The angle of elevation of the top of the tower from her eyes is 60°. Find the height of the tower .

(i)

152.17 m
(ii)

132.17 m
(iii)

126.17 m
(iv)

155.17 m
(v)

140.17 m

Question 7

7.

A man in a boat rowing away from a lighthouse 65 m high, takes 0.5 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.

(i)

0.59 m/sec
(ii)

3.59 m/sec
(iii)

2.59 m/sec
(iv)

9.59 m/sec
(v)

1.59 m/sec

Question 8

8.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
30°
.
If the distance between the point and the foot of the
building
is
190 m
,
find the height of the
building
.

(i)

190
3

√

18

m
(ii)

95

√

2

m
(iii)

190
3

√

3

m
(iv)

190
3

m
(v)

190

m

Question 9

9.

From a point 150 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the cliff.

(i)

81.61 m
(ii)

86.61 m
(iii)

89.61 m
(iv)

83.61 m
(v)

91.61 m

Question 10

10.

From the top of a light house which is 75 m high from the sea level, the angles of depression of two ships are 60° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.

(i)

91.59 m
(ii)

83.59 m
(iii)

89.59 m
(iv)

86.59 m
(v)

81.59 m

Question 11

11.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 90 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the height of the other temple.

(i)

35.03 m
(ii)

33.03 m
(iii)

41.03 m
(iv)

43.03 m
(v)

38.03 m

Question 12

12.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the flag staff is 15 m, find the height of the building .

(i)

15.49 m
(ii)

23.49 m
(iii)

17.49 m
(iv)

20.49 m
(v)

25.49 m

Question 13

13.

A person, walking 35 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 60°. Find the height of the flagpost .

(i)

35
2

√

18

m
(ii)

105
2

m
(iii)

35
2

√

3

m
(iv)

105
4

√

2

m
(v)

35
2

m

Question 14

14.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 90 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the width of the river .

(i)

87.00 m
(ii)

93.00 m
(iii)

85.00 m
(iv)

90.00 m
(v)

95.00 m

Question 15

15.

The shadow of a vertical tower BA on a level ground is increased by 40 m, when the altitude of the sun changes from 45° to 30°. Find the height of the tower .

(i)

59.65 m
(ii)

54.65 m
(iii)

49.65 m
(iv)

51.65 m
(v)

57.65 m

Question 16

16.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
60°
.
If the distance between the point and the top of the
chimney
is
40 m
,
find the height of the
chimney
.

(i)

20

√

18

m
(ii)

30

√

2

m
(iii)

20

√

3

m
(iv)

60

m
(v)

20

m

Question 17

17.

From a point 50 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 45° respectively. Find the height of the pillar.

(i)

33.61 m
(ii)

41.61 m
(iii)

36.61 m
(iv)

31.61 m
(v)

39.61 m

Question 18

18.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
30°
.
If the height of the
building
is
100 m
,
find the distance between
the observation point and the foot of the
building
.

(i)

300

m
(ii)

100

√

3

m
(iii)

150

√

2

m
(iv)

100

√

18

m
(v)

100

m

Question 19

19.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
30°
.
If the height of the
radio tower
is
40 m
,
find the distance between
the observation point and the top of the
radio tower
.

(i)

79

m
(ii)

77

m
(iii)

81

m
(iv)

82

m
(v)

80

m

Question 20

20.

Two poles of equal height are standing opposite to each other on either side of a road which is 15 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 45° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

4.49 m

, distances away =

4.49 m

,

8.51 m
(ii)
height =

6.49 m

, distances away =

6.49 m

,

10.51 m
(iii)
height =

7.49 m

, distances away =

7.49 m

,

11.51 m
(iv)
height =

3.49 m

, distances away =

3.49 m

,

7.51 m
(v)
height =

5.49 m

, distances away =

5.49 m

,

9.51 m

Question 21

21.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 30° with the ground. The top of the tree touches the ground at a distance of 80 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

138.57 m
(ii)

123.57 m
(iii)

112.57 m
(iv)

152.57 m
(v)

166.57 m

Question 22

22.

Two boys are on opposite sides of a tower of 10 m height. They measure the angle of elevation of the top of the tower as 30° and 45° respectively. Find the distance between the two boys.

(i)

(

10

√

18

+

10

√

6

)

m
(ii)

(

10

√

3

+

10

)

m
(iii)

200

m
(iv)

(

2

+

√

3

)

m
(v)

(

15

√

2

+

5

√

6

)

m

Question 23

23.

The angles of depression of two boats from the top of a cliff 70 m high are 60° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

95.42 m
(ii)

118.42 m
(iii)

110.42 m
(iv)

138.42 m
(v)

107.42 m

Question 24

24.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
60°
.
If the distance between the point and the foot of the
tower
is
180 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

359

m
(ii)

358

m
(iii)

362

m
(iv)

360

m
(v)

361

m

Question 25

25.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the building is 7 m, find the height of the flag staff .

(i)

7.12 m
(ii)

3.12 m
(iii)

6.12 m
(iv)

5.12 m
(v)

4.12 m

Assignment Key